Nonparametric Regression And Asymptotic Properties Of Two Kinds Of Data

This paper will mainly study nonparametric regression model and asymptoticproperties of dependent data in errors-in-variables and spatial data. For the free form ofregression function and fewer limits to random variable, nonparametric regression modelis widely used in practical problems, and has great research value in economic, financialand social sciences. Therefore, it's very important to research nonparametric regressionmodel and asymptotic properties of dependent data and spatial data in-depth, particularlyand widely. This paper will focus on the following aspects.Firstly, the paper will introduce the nonparametric statistical methods after theparametric statistical ones. It will introduce the basic concept of parametric regressionmodel, nonparametric regression model and their research situation at home and abroadand discuss the evolution from parametric model to nonparametric model, the form ofnonparametric model, weight function and its consistency of moment, density kernelestimation, the concept of kernel and kernel regression estimation. Besides, the best choiceof theoretical bandwidth, staggered identification of sample bandwidth and experienceselection method of bandwidth as well as the concept of linear smoother will be alsointroduced in this paper.Secondly, a further study on the basis of a series of deconvolution kernel techniqueswill be carried out. It will make some assumptions and obtain the related lemmas. Anddraw a conclusion for the short-range dependent(SRD) and the long-rangedependent(LRD) data in ordinary smooth. By giving the necessary assumptions in asuper-smooth case, the paper will discuss the asymptotic variance of the local constantestimator and show the effect of LRD appears in variance.Thirdly, it is pointed out that the conditional mean of a dependent variable, givenexplanatory ones, is a nonparametric function if the nonparametric regression with spatialdatea is considered. The conditional covariance reflects the spatial correlation. Besides,the paper will discuss a linear process for disturbances, allowing for long-range, as well asshort-range, dependence. And it will also give a description of the dependence explanatory variables from the aspect of joint density and marginal density.Finally, under sufficient conditions, the paper will discuss the consistency andasymptotic normality of kernel regression estimates. The central limit theorem isestablished and the weak dependence of the asymptotic variance is obtained when theobservations are independent.